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Quiz 2: Sinusoidal functions and proportionality

Last unanswered question  Question  Next unanswered question
 

Question 1

 
 
Which of the following correctly describes the function shown ?
PIC
a) 4 3π y = 2cos (x - --) 3 8
b) 4 y = 2sin 3x
c) A sinusoidal function with amplitude 2, period 3π- 2 and mean level 0.
d) All of the above.

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
 

Question 2

 
 
Find the amplitude and the mean level of the function 2π f(x) = 2 sin--(x- 4)+ 1 3 .
a) Amplitude = 1, mean value = 2.
b) Amplitude = 2, mean value = 1.
c) Amplitude = 3, mean value = 4.
d) Amplitude = 4, mean value = 3.

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 3

 
 
Find the period of the function f(x) = 2sin 2π-(x - 4)+ 1 3 .
a) 2π -3-   b) -3- 2π
c) 1 - 3   d) 3

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
Period = 2π 2π ∕---= 3 3 .
 

Question 4

 
 
Find the period and the amplitude of the function f(x) = 4sin(3x - 5) + π.
a) Amplitude = 4, period = 2π.
b) Amplitude = 5, period = 2π.
c) Amplitude = 4, period = 2π- 3.
d) Amplitude = 5, period = 2π --- 3.

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
 

Question 5

 
 
If y = 4sin(3x - π) + 5, which of the following is true ?
a) -4 ≤ y ≤ 4   b) 1 ≤ y ≤ 9
c) 1 ≤ y ≤ 5   d) -4 ≤ y ≤ 9

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 6

 
 
Which of the following has period π 2- and amplitude 4 ?
a) y = 4sin4x   b) π- y = 4cos2 x
c) π y = --sin4x 2   d) y = 4cos4x

 

Your answer is correct.
Note that 4 is also correct.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
Note that 1 is also correct.
 

Question 7

 
 
Which of the following has period 2 and amplitude 3 ?
a) y = 2sin3x   b) y = 3cos2x
c) y = 2sinπx   d) y = 3cosπx

 

Not correct. Choice (a) is false.
1 has amplitude 2, period 2π3-.
Not correct. Choice (b) is false.
2 has amplitude 3, period π.
Not correct. Choice (c) is false.
3 has amplitude 2, period 2.
Your answer is correct.
 

Question 8

 
 
Which of the following has period 4π and amplitude 1 2 and is such that f(0) = 1 2 ?
a) 1 y = 2 sin 4x   b) 1 1 y = - cos -x 2 2
c) 1 1 y = 2 sin2 x   d) 1 y = 2 cos4x

 

Not correct. Choice (a) is false.
1 has amplitude 1 2 , period π- 2 .
Your answer is correct.
Not correct. Choice (c) is false.
3 has amplitude 1 2 , period 4π, but f(0) = 0.
Not correct. Choice (d) is false.
4 has period 12, period π- 2 .
 

Question 9

 
 
Expand π- sin2(x+ 3 ) .
a) √ - --3cos2x + 1sin 2x 2 2   b) √ - --3 cos2x - 1 sin2x 2 2
c) √ - --3 sin2x + 1cos2x 2 2   d) √ - --3 sin2x - 1cos2x 2 2

 

Not correct. Choice (a) is false.
Your answer is correct.
sin2(x+ π-) = sin(2x+ 2π-) 3 3 = sin2x cos 2π-+ cos2x sin 2π 3 √ - 3 1 --3 = -2 sin 2x+ 2 cos2x
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 10

 
 
The sinusoidal function f is illustrated below.
PIC
The function g has mean level 0, amplitude half that of f, and period twice that of f. Find the equation for the function g.
a) 3 g(x) = 2 cos 2x   b) g(x) = 3cosπx
c) g(x) = 3cosπx 2   d) g(x) = 3cos2x

 

Your answer is correct.
Since f has period π2 and amplitude 3, g must have amplitude 32 and period π.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.